How can I quickly manage visibility of channels across multiple objects in the graph editor
You can edit curves only for selected objects, or filter unneded curves by various types.

Hide channels for other objects
Enable Only Include channels relating to selected objects and data in the Graph Editor header. With this enabled you can edit channels of only selected objects which decreases amount of data to handle with.



Filtering channels

Filtering by type
Enable Filters in the window header. From there select which type of animation data is desired to be shown, from 8 categories of animation data: scene, world, nodes, objects transforms, meshes, datablocks related to modifiers, lamps and cameras. Click LMB to select / deselect multiple:



Only transfroms animation data is shown above because it is what location / rotation keyframes of objects are.

Filter by keyword
Enable filtering by keyword; the filter will be applied while you type it in.



"X" is typed as keyword; shown all keyframes which have letter X in their property.

Visibility of channels

Also it's possible to hide all but selected channel, see shortcut to show a single channel (solo mode) in the graph editor ?, or disable visibility for multiple channels.
You could do that quickly by clicking Eye icon of one channel and hover it over Eye icons of other channels up / down without releasing the mouse. The channels will be hidden.